We utilize scanning confocal fluorescence microscopy to interrogate single fluorescent lipid molecules in unsupported planar bilayers. At high photon flux, an optical trapping effect appears that is approximately 100,000 times larger than predicted by theory. We hypothesize that the enhancement results from confining molecules of resonantly large polarizability in a two-dimensional viscous fluid. Interestingly, the laser appears to direct the diffusive motion of individual fluorophores as the beam scans across the membrane plane. Single lipid molecules track with the laser farther, and with greater directional uniformity, than simple Einsteinian diffusion allows. We present evidence from experiment and simulation that reveals the enhanced trapping effect.